In[]:=
rho=1000;​​ΔP=0.008;​​L=2;​​R=0.15;​​n=0.748;​​λ=0.47;​​μ0=20.0510^-3;​​
μ
∞
=0;​​ω=0.1;​​system[r_]:={D[r(μ0(1+(λD[v[r],{r,1}])^2)^((n-1)/2)D[v[r],{r,1}]),{r,1}]-ΔP/Lr,v[R]0,v'[10^-7]0};​​rs=NDSolve[system[r],{v},{r,10^-7,R},MaxSteps10000];​​valR=Range[10^-7,R,3.061222449*10^-3];​​valV=Table[v[r]/.rs/.r->rVal,{rVal,valR}]​​
Out[]=
{{0.0011222},{0.00112171},{0.00112031},{0.00111797},{0.0011147},{0.00111049},{0.00110535},{0.00109927},{0.00109226},{0.00108432},{0.00107544},{0.00106562},{0.00105487},{0.00104319},{0.00103057},{0.00101701},{0.00100252},{0.000987101},{0.000970742},{0.000953449},{0.000935221},{0.000916058},{0.000895961},{0.000874928},{0.000852961},{0.000830059},{0.000806222},{0.000781451},{0.000755744},{0.000729103},{0.000701527},{0.000673017},{0.000643571},{0.000613191},{0.000581876},{0.000549627},{0.000516442},{0.000482323},{0.000447269},{0.00041128},{0.000374356},{0.000336498},{0.000297704},{0.000257976},{0.000217314},{0.000175716},{0.000133184},{0.0000897166},{0.0000453147}}
eqdiff={r*(rho*D[u[r,t],{t,1}]+((-ΔP/L*Cos[ω*t])))==D[r(μ0(1+(λD[u[r,t],{r,1}])^2)^((n-1)/2)D[u[r,t],{r,1}]),{r,1}],u[r,0]==valV,u[R,t]0,(D[u[r,t],r]==0)/.r->10^-7};​​NDSolve[eqdiff,{u[r,t]},{r,10^-7,R},{t,0,30}]
NDSolve`FiniteDifferenceDerivativeFunction
::ddim
:Data {{0.0011222},{0.00112171},{0.00112031},{0.00111797},{0.0011147},{0.00111049},{0.00110535},{0.00109927},{0.00109226},{0.00108432},39} is not a rectangular tensor with dimensions {49}.
​
NDSolve`FiniteDifferenceDerivativeFunction
::ddim
:Data {{0.0011222},{0.00112171},{0.00112031},{0.00111797},{0.0011147},{0.00111049},{0.00110535},{0.00109927},{0.00109226},{0.00108432},39} is not a rectangular tensor with dimensions {49}.
​
NDSolve`FiniteDifferenceDerivativeFunction
::ddim
:Data {{0.0011222},{0.00112171},{0.00112031},{0.00111797},{0.0011147},{0.00111049},{0.00110535},{0.00109927},{0.00109226},{0.00108432},39} is not a rectangular tensor with dimensions {49}.
​
General
:Further output of NDSolve`FiniteDifferenceDerivativeFunction::ddim will be suppressed during this calculation.
Set
:Cannot take positions 1 through 3 in Abs[1].
Set
:Cannot take positions -3 through -1 in Abs[1].
Set
:Cannot take positions 1 through 3 in Abs[1].
General
:Further output of Set::take will be suppressed during this calculation.
NDSolve
:Encountered non-numerical value for a derivative at t == 0..
Out[]=
NDSolver-0.004Cos[0.1t]+1000
(0,1)
u
[r,t]
0.02005
(1,0)
u
[r,t]
0.126
1+0.2209
2
(1,0)
u
[r,t]

-
0.00111612r
2
(1,0)
u
[r,t]
(2,0)
u
[r,t]
1.126
1+0.2209
2
(1,0)
u
[r,t]

+
0.02005r
(2,0)
u
[r,t]
0.126
1+0.2209
2
(1,0)
u
[r,t]

,u[r,0]{{0.0011222},{0.00112171},{0.00112031},{0.00111797},{0.0011147},{0.00111049},{0.00110535},{0.00109927},{0.00109226},{0.00108432},{0.00107544},{0.00106562},{0.00105487},{0.00104319},{0.00103057},{0.00101701},{0.00100252},{0.000987101},{0.000970742},{0.000953449},{0.000935221},{0.000916058},{0.000895961},{0.000874928},{0.000852961},{0.000830059},{0.000806222},{0.000781451},{0.000755744},{0.000729103},{0.000701527},{0.000673017},{0.000643571},{0.000613191},{0.000581876},{0.000549627},{0.000516442},{0.000482323},{0.000447269},{0.00041128},{0.000374356},{0.000336498},{0.000297704},{0.000257976},{0.000217314},{0.000175716},{0.000133184},{0.0000897166},{0.0000453147}},u[0.15,t]0,
(1,0)
u

1
10000000
,t0,{u[r,t]},r,
1
10000000
,0.15,{t,0,30}